The microeconomics of “Deal or No Deal”

Every economics nerd in the country had to be ecstatic when they tuned in to watch NBC’s “Deal or No Deal”. After watching the show for all of two minutes I turned to my wife and exclaimed something about it being a great example of microeconomic theory. She rolled her eyes. I programmed the TiVo.

The show is a game show format. A contestant chooses one of 26 different briefcases. Each briefcase contains a dollar amount between $.01 and $1,000,000. The contestant then participates in a series of rounds where the amounts inside the other briefcases are revealed. After each round, the “banker” offers the contestant a dollar amount to buy the briefcase back. The contestant then has to decide whether to continue to the next round or take the offered amount of money. If the numbers revealed in the next round are high numbers, the banker’s offer will decrease. If, however, the opposite occurs and lower numbers are revealed the briefcase is assumed to have a higher value and the banker will increase their offer.

You do not have to be an economics nerd like myself to enjoy the show, but it certainly makes the game more entertaining. Take, for example, Tuesday night’s first contestant. He was down to six numbers left: $300. 700. 10,000. 300,000. 400,000. 500,000. The offer from the banker was $99,000. Would you take the offer?

Using microeconomic theory, one could calculate that the expected value was roughly $201,841. Whether or not he should take the amount depends on his utility. Theory tells us that we cannot calculate utility in everyday life, but in this case we can get an idea. If he chose to continue then we could safely assume that his expected utility of $201,841 is greater than his utility of $99,000.

The contestant showed rejected the offer and continued to reject other offers. When there were only four numbers remaining the contestant was offered $240,000. The numbers remaining were: 10,000. 300,000. 400,000. 500,000. The expected value in this case was $302,500. He continued and his fiancé screamed, “I cannot believe he’s going for it.” I on the other hand could believe it. It was a simple matter of utility. The next box was revealed to be $500,000. Now the expected value was approximately $236,666. The offer was now reduced to $189,000. He accepted this offer.

So what do these results tell us about the contestant? This tells us that this particular contestant has a Friedman-Savage utility function. For non-nerds this means that he is risk seeking with respect to a large gamble and risk averse with respect to a small gamble. In this case, he was willing to give up $99,000 because his expected value was more than twice that amount. However, when offered $189,000 he was unwilling to continue because the expected value was not much higher.

“Deal or No Deal” is a prime example of microeconomic theory at work. If the show lasts long enough (and I hope that it does), it could be a useful tool for more expansive studies of the relationship between risk and utility. In the meantime, I will continue watching the show while my wife rolls her eyes. Oh, and for those of you wondering, the contestant’s briefcase contained the value of $10,000.

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16 responses to “The microeconomics of “Deal or No Deal””

The game was developed and first aired in the Netherlands in 2002, where it continues to run as a blockbuster. The money amounts there are even bigger than in the US, with a max of 5,000,000 euro. Erasmus School of Economics has a working paper on this show that reveals strong support for the behavioral “break-even-effect” of Thaler and Johnson. See

ssrn.com/abstract=636508

The interesting thing about this show is that it uses a series of gambles and thus shows the effect of previous outcomes. In the Dutch episodes, many unfortunate contestants, who openend the valuable briefcases, reject bank offers in excess of the expected prize, i.e., behave as risk seekers (rather than risk averters). It would be interesting to see if this also happens with US contestants.

There is no risk whatsoever associated with this show. I have been reading articles everywhere about economists studying relative risk-aversion and risk assessment. To have risk, people need to be sacrificing something, not money they either did not start with, or do not have yet (until they press that button). This is the equivalent of studying risk in how people play online poker without using real money.

There is risk associated. If they reject the offer, they have given up the money value of the offer. You are simply looking at this from a different point of view.

For example, if an individual receives an offer of $75,000, but chooses to continue, they have given up that value in hopes of winning more. There is significant risk involved as they may never be able to attain that offer again.

In economics, risk refers to both downside and upside uncertainty. So a gamble that will either return $5 or $10 is still considered risky. Furthermore, contestants assume down-side risk when they refuse a banker’s offer.

This is all very intersesting information and I am curious as to whether you think the Banker uses some type of algorithum or equation to figure out his offer. It is hard for me to imagine that the people who pay out the money trust the gut instinct of the banker to make a good offer. Sure he can figure out the expected value but does he then use that to figure out a more accurate, relevant offer that will make the contestant think.

It seems to me that the banker discounts the likelihood that the case contains a relatively large value if there are a lot of cases left. This is evidenced by the fact that so often the early game offers by the bank are less than the arithmetic mean. As the game continues, the offers seem to approach then exceed the mean of the remaining numbers as long as the board is not weighted too heavily towards low values. For example, in a recent episode where the values were doubled, the contestant had three sub $1000 cases left, $50,000, $100,000, and $2,000,000. However, she was only offered ~$80,000 (the mean of this group being in excess of $350,000) which represents a heavy discount on the average on the basis of the low values being overweighted. So a good equation for finding out what the bank is going to offer may look something like this:

Bank Offer=f{x,[g(n,v)]}

where x represents the a ratio or weight between relatively high and low values (many low values = more risk averse bank), n the number of cases left, and v the values remaining. The function g may very well be the expected value or arithmetic mean, but I have no idea what the function f may be. As an interesting note, because the bank can become more or less risk averse, the bank is not assuming infinite iterations of the game or it has the goal of making a profit. Also the three door problem may factor into this too, as the contestant does not have a 1/n or 1/26 chance that there case contains the maximum value after the first round of the game. Likely it is somewhere in between.

Those who believe there is no risk or economics involved in the show please STFU, I’m not even going to waste my time explaining it to you. However, there is one interesting dilemma in trying to figure out the banker’s logic in his offers. The show has to last for an hour, therefore you can’t necessarily assume his offers are rational. I’d like to talk to the producers…

It seemed to me that the banker’s offers were pretty close to the average value of the remaining cases, no?

I’m a neuroscientist studying the neural substrates of “reward”- came across microeconomic utility theory (seems that aspects of such decision-making has neural correlates), and then it dawned on me: deal or no deal! Still trying to grasp the difference between ‘expected utility’ and ‘expected value’…

Would anyone be able to explain this for me?
I’d really appreciate it.

Oh, sorry- banker’s offers are quite different to the mean, which would be the same as the expected value, since each case is of equal probability. I get expected utility and expected value now, thanks.

It does involve in risk, but expected value does not explain his expected utility. Furthermore, charateristic and personal background plays an important role in here too. If people comes for fun, his reference point will be much different compared to people plays for money. Those who judge his reference point is 0$ entry to get in will take much risk compared to those think $99k is a reference point. In some research, they find that risk averse person feel much worse when they lose compared to the same size gain in the ratio approximately 2.5:1, which means that the utility u gain for earning 2.5$ is just equal the disutility when u lost 1$. This could somehow explain the value of the offer.